Math Is Fun Forum

Mellyyy

Guest

Venn diagrams

How would you do this question using a venn diagram?
107 people attended a conference
- 66 are married
- 55 are over 40 years old
- 36 are married femaes and 21 of these are over 40 years old
- 28 are females who are over 40 years old
- 17 are married males who are over 40 years of age which is three more than the number of unmarried females who are not over 40

John E. Franklin

Member

Registered: 2005-08-29

Posts: 3,588

Re: Venn diagrams

Make 3 circles that overlap in the middle, so it makes
a 3 petal daisy in the overlap.

Notice there are 3 categories, each having opposites with them:
1a. married   
1b. unmarried
2a. over 40 
2b.  under 40
3a. female 
3b.  male

Now there are 3 big circles.
Look at each one separately, and forget about the other ones.
Make the inside of one circle to mean 1b, and make the outside of
that circle to mean 1a.
Look at another circle, and make the inside of it 2b, and the outside
of it, everywhere outside of it including parts of the other circles,
will be 2a.
And for the last big circle, make the inside mean 3b, and the outside
of it to be 3a.
Also, it is totally up to you whether the "a" or the "b" goes inside or outside,
you decide.

Outside of all three circles, is 1aAND2aAND3a.
Inside of all three circles in the middle of the daisy is 1bAND2bAND3b.
All 3 things are true at the same time.

But in the 3 petals of the flower, you have only two "b's" and one "a".
This is because you are inside two circles (the b's) and outside of one of
the circles (an "a").

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